Course Of Descriptive Geometry Research Articles

Начертательная геометрия сегодня: проблемы и перспективы

Against the background of constant reduction of the time allocated for contact work with students in curricula, there are discussions on the necessity of teaching some disciplines in universities, and their list is constantly changing. In the current case, the current round of discussion is connected with the signing of the decree on the reform by the President of Russia V.V. Putin. Putin signed a decree on the reform of higher education. Now it is a pilot project, which will be tested in several universities for three years. It is about the transition of engineering training from bachelor's degree to specialization. The reform will require considerable efforts to develop new curricula, adjust the list of academic disciplines included in them. Simultaneously with the inclusion of modern disciplines into this list, the process of excluding obsolete and irrelevant disciplines is underway.
 
 According to the experience of the past years, disciplines of the general engineering cycle are constantly subjected to "reforms". In the case of technical specialties, descriptive geometry is a permanent outsider [8, 28]. The developers of the Federal State Educational Standards of Higher Education (FSES HE), who announced a competency-based approach to the learning process and assessment of knowledge of university graduates, probably also hold the opinion that descriptive geometry is a "dying" discipline.
 
 The purpose of the authors of the article is an attempt to look at the problem not from the point of view of the age of descriptive geometry, but only guided by the frequency and efficiency of its methods in engineering practice and modeling of geometric objects of spaces of dimension 2+ and more.
 
 The set goal required the solution of several problems. One of them is to clarify the question of what exactly the reformers are trying to do. Is it to remove an academic discipline or a section of mathematics, which is, in fact, descriptive geometry, from the course of engineers' training? It is also necessary to find out for which specialties or directions the descriptive geometry course is superfluous or obsolete.

Some Results and Evaluation of Training for the Development of Students’ Spatial Visualization

This article discusses the results and evaluation of a training course focused on developing spatial visualization using interactive dynamic tools. The course aims to effectively integrate technology with the Descriptive Geometry course by combining content, pedagogy, and technology while considering the course's characteristics. The training course consists of three phases: seeing, imagining, and drawing. Each phase has different tasks that involve manipulating 3D objects in a virtual environment, corresponding to the level of geometric thinking and cognitive steps of mental rotation. The results of the organized training showed a statistically significant increase in student's spatial skills, and the evaluation of students using the SURE (Structure-Oriented Evaluation) model was deemed sufficient.

Innovation in engineering education using AR technology on the example of disciplines “Descriptive Geometry” and “Engineering Graphics”

Research relevance. With the use of computer-electronic-digital equipment, the achievements of scientific and technological progress become part of education. This obliges to improve the field of education: to change and create the forms and content of education, methods and approaches to the educational process, to increase the volume and quality of knowledge. Augmented reality favors autonomous learning by using mobile devices, simplifies the understanding and interpretation of geometric shapes and contributes to the development of students' spatial thinking. The research purpose is to form new knowledge, skills and abilities for the convergence of the real and digital worlds based on the possibility of using augmented reality technology, to determine the reasons that make it difficult for users to accept information technology as an educational tool. Materials and methods. Scientific papers published between 2013 and 2022 in the scientometric databases Scopus, Web of Science, Google Scholar, E-library were considered, pedagogical experience on the research topic was studied; various types of diagnostics of students were taken into account with summing up the outcomes and the results of theoretical and practical research were summarized. A practical study of the problem was carried out by creating a 3D model of octants and projections of points. Research results. An augmented reality application was created on the Unity 2018.4.12f1 platform with additional modules – Vuforia Augmented Reality Support and Android Build Support. When developing the application, the authors created 3D models of octants, projections of points in the SketchUp program. A survey on conscious understanding and mastering the descriptive geometry course showed that the majority of students showed positive dynamics in mastering the descriptive geometry course. Conclusion. As a result of using a specially developed application based on the augmented reality platform, it is possible to move from standardized educational trajectories to individual ones, which significantly increases the effectiveness of modes of study and restructuring of the educational process.

Повышение наглядности представления изучаемых в начертательной геометрии объектов

Increasing the visibility of representation for objects studying in the process of solving basic problems related to descriptive geometry (DG) significantly improves the understanding and perception of the discipline by students. A team of authors representing St. Petersburg Mining University’s DG and Graphics Chair developed their own projects, which are interactive graphics that allow teachers to visualize the solution of some DG course’s problems directly during academic studies. Projects have been created by the Wolfram Mathematica (WM) system tools and divided into 7 sections: points, lines, planes, geometric elements’ mutual position; relative position of a straight line and a second order surface; relative position of a plane and a second order surface; relative position of second order surfaces; mutual position of revolution bodies and polyhedrons; relative position of polyhedrons; a tangent plane to a second-order surface. Difficulties that have arisen in the work, ideas and possibilities for further implementation of proposed principles for using computational WM algorithms when creating and employing these projects in the process of students’ geometric-graphic training are discussed. It is noted that WM allows you manipulate data and observe how the result is changing dynamically, that certainly makes it possible and is an advantage of WM for using it in students’ geometric-graphic teaching. Lecturers of DG and Graphics Chairs can: use the proposed in this work projects aimed at implement various graphic constructions for both preparation of academic studies and in real-time mode during them; create elements of information supply for the educational process; develop demonstration support for academic studies, that in turn will ensure the proper material assimilation by students.

IMPACT OF DESCRIPTIVE GEOMETRY ON THE IMPROVEMENT OF SPATIAL ABILITIES OF ARCHITECTURE STUDENTS

Spatial intelligence is an important skill for students of technical faculties, especially those fields where the capacity for engineering thinking and creative expression is equally valued. The field of Architecture is emphasized here, and the issue of assessing the spatial abilities of architecture students and their improvement has often been observed. This paper will examine the impact of the course of descriptive geometry on the development of their spatial thinking, and whether there is progress between the initial spatial abilities with which students were enrolled and abilities after completing the first semester of study.

Kesalahan Konsep Descriptive Geometry Mahasiswa terhadap Kemampuan Spasial dalam Pembelajaran Daring di Masa Pandemi COVID-19

Spatial ability is one of the essential abilities to be mastered by students, especially in geometry. There is not much research, especially in Indonesian, that examines students' spatial abilities and their relation to Descriptive Geometry. This study aims to analyze students' misconceptions in the Descriptive Geometry course and describe the profile of students' spatial abilities in online learning during the COVID-19 pandemic. This study's subjects from the Mathematics Education Department of Universitas Negeri Jakarta. This research is descriptive qualitative. The learning was carried out in 16 meetings with three initial meetings offline, and the next 13 meetings online. The test was given twice at the 8th and 16th meetings accompanied by interviews with students who made mistakes in taking the test. The test results showed that students who made mistakes did not have the ability to spatial perception, spatial relation, and spatial orientation. However, there was a case of students who made mistakes still having the ability to spatial perception, spatial relation, and spatial orientation. The obstacles that affect students' spatial abilities are online learning that is not supported by technical matters, namely: limited internet networks and internet quota availability.

Innovative Course of Descriptive Geometry

The paper deals with the solution to the problems of insufficient preparation of applicants for the study of the Descriptive Geometry course offered to them in the university during their first year of education in such programs of study as Mechanical Engineering, Automation of Technological Production Processes, Mechatronics and Robotics, as well as Oil and Gas Engineering. The relevance, efficiency and advantages of an innovative course using AutoCAD and new teaching material for independent work of both Russian and foreign students were evaluated. Algorithms for the construction of 3D models of intersecting tangent surfaces and surfaces with a common inscribed sphere were developed to control individual tasks. The tasks of two-level complexity of constructing projections of parts with surfaces intersecting along curved lines and their 3D models with sections for monitoring the retained knowledge of students on the subject were developed and the effectiveness of their application was evaluated.

Surface Modeling in the Course of Engineering Graphics

Development of the designer’s documentation package by means of CAD systems implies good skills with toolkits of solid and surface modeling. The ability to identify the surface type, its generation process and consequently to choose the optimal modeling is acquired in the descriptive geometry course, as well as engineering graphics and computer graphics courses. The article describes training assignments designed for students of machine building departments aimed both at consolidation of theoretical knowledge and development of skills required to identify and model various surface types.

A modified design-analog method of teaching geometry and graphics as a means of integrating of training and design activities of future architects

The strategy of teaching orthogonal and other projections, as well as the basics of geometry formation of the future architect is based on the practical orientation of the teaching process and is based on a modified design-analog method. Possibilities of the building industry show an urgency of research and realization of methods of shaping geometry in a course of descriptive geometry. The purpose of the study is to develop technology for the formation of design skills of shaping, based on the proposed modified design and analogue method. The object of research is geometrical and graphic training of students pursuing the degree in Architecture or Design of architectural environment. The subject of study is the technology of training of shaping in the course of descriptive geometry and based on a modified design-analog method. The characteristic feature of this method is its connection with the architectural practice of both educational and professional. The methodological basis for its application is the method of creating of the architectural form of an object. The workshop has been tested and allowed to consider a set of actions and operations, their sequence.

On the Issue of Practical Orientation of Teaching Students of Technical Universities the Basics of Descriptive Geometry

Purpose of the research. The introduction of a distance education system in the form of an electronic educational environment in modern conditions requires new approaches to increasing the interest of students in learning the material. This is especially true for general education subjects. One of the ways to improve the efficiency of learning disciplines is to link theory with practice. In addition, traditional practical tasks on subjects of the general education cycle do not fully take into account the application of the acquired knowledge in the future professional activity of students. Therefore, the purpose of this work is to study the methodology and develop solutions to tasks that most fully take into account the practical orientation of the studied subjects of the general education cycle in technical universities. Materials and methods. As the object of research, the course of descriptive geometry was chosen as the most difficult subject for students of the first year of higher educational institutions of technical direction. Based on the analysis of the structure of the discipline “descriptive geometry and engineering graphics", the authors propose to link the practical part of the course to a specific technical device. Then, using the accepted assumptions, theoretical positions and goals of studying descriptive geometry, we need to develop a set of interrelated tasks that describe the design of a technical device and the interaction of its elements, allowing you to develop the initial skills of the student with mechanical drawings manually, as well as through computer programs both standard and developed by lecturers of the Department “Descriptive Geometry and Graphics " of the Penza State University of Architecture and Construction. Results. The article presents the results of applying the practical orientation of the theoretical provisions of descriptive geometry for students studying in the direction of “Operation of transport and technological machines and complexes" of the Penza State University of Architecture and Construction. As a visual technical device, the liquid supply regulator, used in automotive equipment is selected. Essentially practical orientation is to solve three interrelated problems to determine controller parameters by the methods of descriptive geometry: relative position of subassemblies of the regulator (integrated positional task); determination of the actual values of the elements of the regulator (how to convert a drawing); characterization of the body of the regulator for creation of the flask when casting (intersection of the surfaces and scan one of the bodies coated with line-crossing). The results of solving the tasks are presented in the form of calculation and graphic works and laid out in the electronic environment of distance learning, as the final report documents for the study of the main sections of the course of descriptive geometry. The lecturer places examples of calculation and graphic works’ implementation in the electronic educational environment, features of formation of initial skills for drawing and reading machine-building drawings, and students upload their decisions to the page of the corresponding course in stages or the work performed as a whole.Conclusion. In the final part of the article, conclusions are formulated based on the results of the research, made by the authors. The conclusions reflect the ways to achieve the goals of studying descriptive geometry using computer technologies and e-education. In addition, the uniqueness and results of using the proposed method in a technical University are shown.

Анализ некоторых задач курса теоретической механики, решаемых методами начертательной геометрии

In this paper the usability of descriptive geometry’s methods for solution problems related to theoretical mechanics is considered. Descriptive geometry emerged as a science intended for solution the problems of human activity’s different branches. In connection with development of modern graphical means, the value of descriptive geometry is greatly underestimated, but it is on descriptive geometry’s principles and laws that have been built algorithms used in graphic applications [30]. For a long time descriptive geometry has been used by scientists in various spheres of human activity [27]. In study of general technical disciplines, interdisciplinary connections play an important role, especially between theoretical disciplines, whose understanding is particularly difficult for students [35]. Understanding the possibility of using descriptive geometry’s methods, students can think over aspects of their use in the performance of tasks under study, for example, theoretical mechanics. Methods, which can be use while solving problems from the course of theoretical mechanics, are learned by students in the standard course of descriptive geometry and are not particularly difficult. Therefore, the graphical approach to solving problems of theoretical mechanics is accessible and understandable for majority of successful students. In this paper example problems from the course of theoretical mechanics on the topics "Plane System of Forces" and "Spatial System of Forces" have been considered. Graphical problem solving was performed using the image of force vectors with the help of orthogonal projections. For checking the correctness of graphicalcons.

FROM PERSPECTIVE DRAWING TO LOW COST PHOTOGRAMMETRY: APPLICATION IN ARCHITECTURAL STUDIES

Abstract. Nowadays digital tools are booming. The evolution of the technologies used in archeology and in architecture is such that we are going more and more towards low cost and time saving. Indeed, today we can use free softwares in photogrammetry in order to make 3D surveys of architectural buildings. Fifteen years ago it only required the use of the 3D laser scanner, a very expensive technique.As part of the course reform of the second year at the national school of architecture and urban planning Tunisia in the course of descriptive geometry and perspective drawing, an experiment was conducted in order to introduce low cost photogrammetry using the free software 123 D catch by autodesk, 3DF Zephyr or Scann 3D on the mobile phone. The objective of this course is to make students experiment different techniques of representation such as photogrammetry, perspective drawing, using a mobile phone , a digital camera or a pen. The object of the representation is the Tunisian cultural heritage such as the archeological site of Carthage.

Геометро-графические студенческие олимпиады в Санкт-Петербурге

Two geometric-graphic Olympiads are held in St. Petersburg: the urban Olympiad in descriptive geometry, initiated by BSTU “VOENMECH” since 1979, and the Olympiad called “Engineering Computer Graphics”, conducted by LETI and ITMO. The peculiarity of the Olympiad in descriptive geometry is its democracy. Its content and organization features are supervised by the professional community, which is united by the section “Geometry, Graphics, Design” of the House of Scientists named after M. Gorky. Competition tasks are developed not only by the organizers. Accepted and suggestions of participants. The content of the Olympiad eventually changes, contributing to its development. Thus, at the suggestion of a number of participants, a comprehensive task was introduced to know the main sections of the course, the task of composition of the task. Despite the withdrawal of the course of descriptive geometry from a number of standards, the fundamentals of this discipline are kept up to date with engineering graphics, which ensures participation in the Olympiad of 7–10 leading technical universities of the city. Olympiad in engineering computer graphics can be attributed to the problem: the level of tasks, focused exclusively on the bachelor degree; on the principles of organization (problem bank of tasks, features of the appeals process); authoritarian chairman of the jury. As a result, it was boycotted by universities, which, unlike the winners, show decent results at All-Russian Olympiads. Among the All-Russian Olympiads, the Olympiad held by MIT stands out. The organizers managed to create a complex competition, which included the ability to solve interesting applied problems on an orthogonal drawing, possession of tools for creating three-dimensional models and drawings of technical products. Given the experience of MIT, the need to create in St. Petersburg an alternative computer graphics competition that is not purely instrumental in nature, the GUT organized an Olympiad called “Total Drawing”. This competition, held under the direction of the chairman of the jury of Professor D.Voloshinov, is gaining popularity. The article discusses and analyzes the principles of organization and the content of these competitions, offers for their modernization and development.

Методика подготовки студентов технических вузов графическим дисциплинам

In connection with transition of the higher education system to the bachelor's degree, a number of difficulties has arisen e in the student’s educational schedule. The question is especially acute for disciplines of general education, and a rather large reduction in classroom time has happened. Taking into account the rather low level of students training in the area of drawing, and sometimes its complete absence, due to the abolition of the subject of drawing from the mandatory school program, teachers are faced with more and more tasks on the formation of educational and methodical complexes [3; 6; 15–17; 23]. In this paper has been considered the issue related to complex training in the area of graphic disciplines for students of technical high educational institutions. These disciplines, as is known, are the basis of many special engineering disciplines, such as machine parts, theory of mechanisms and machines and so on. The fundamental component is the design documentation, the possession of which is necessary for a future engineer. Studying the general course of descriptive geometry and engineering graphics is not enough, training should be carried out taking into account the professional orientation and relevant competencies. However, despite the global automation in all areas, it is not necessary to completely abandon the traditional methods of training, for example, in descriptive geometry’s section. This course allows develop students' spatial reasoning [12–14; 19]. Work on descriptive geometry’s tasks gives for a student the opportunity to more clearly understand the projection principles, methods of drawings transformation, formation of complex surfaces, obtaining of visual images by constructing of axonometric projections or performing of a technical drawing. Another question in our opinion is the order for studying the section of engineering graphics, which is more appropriate to study using modern graphics programs [10; 11].

Компетентностный подход в преподавании темы «Касательная плоскость и нормаль»

Qualified presentation of the topic "Tangent Plane and Surface Normal" in terms of competence approach is possible with the proper level for students' attention focusing on both intra-subject and inter-subject relations of descriptive geometry. Intra-subject connections follow from the position that the contingence is a particular (limit) case of intersection. Therefore, the line of intersection of the tangent plane and the surface, or two touching surfaces, has a special point at the tangency point. It is known from differential geometry [1] that this point can be nodal, return, or isolated one. In turn, this point’s appearance depends on differential properties of the surface(s) in this point’s vicinity. That's why, for the competent solution of the considered positional problem account must be also taken of the inter-subject connections for descriptive and differential geometry. In the training courses of descriptive geometry tangent planes are built only to the simplest surfaces, containing, as a rule, the frames of straight lines and circles. Therefore, the tangent plane is defined by two tangents drawn at the tangency point to two such lines. In engineering practice, as such lines are used cross-sections a surface by planes parallel to any two coordinate planes. That is, from the standpoints for the course of higher mathematics, the problem is reduced to calculation for partial derivatives. Although this topic is studied after the course of descriptive geometry, it seems possible to give geometric explanation for computation of partial derivatives in a nutshell. It also seems that the study of this topic will be stimulated by a story about engineering problems, which solution is based on construction of the tangent plane and the normal to the technical surface. In this paper has been presented an example for the use of surface curvature lines for programming of milling processing for 3D-harness surfaces.

Содержание вузовского курса начертательной геометрии в эпоху третьей промышленной революции

A brief journey into the history of industrial revolutions has been presented. It is noted that our society has entered the third industrial revolution’s era. In this regard, the main consequences of the third industrial revolution have been noted. The stages of development for design methods and the basic science providing the design process have been considered. The historical necessity and significance of Gaspar Monge’s descriptive geometry appearance has been considered as well. Modern products design approaches using CAD systems are described. It is stated that design has again returned to three-dimensional space, in fact prior to the Monge’s era, but at a new stage of development. The conclusion is drawn that, taking into account the realities and needs of modern production, it is necessary to modernize the descriptive geometry course for technical high educational institutions. The author's suggestions on course content changing are presented related to extension of one sections and reducing of another ones, taking into account the fact that in real design practice the designer solves geometric problems in three-dimensional space, rather than in a complex drawing. It is noted that in connection with the extensive use of CAD systems, the design stages and the composition of design documentation developed at each stage are changed. Such concepts as "electronic model" and "electronic document" have appeared and are widely used, that is confirmed by adoption of new USDD standards. In such a case the role and significance of some types of drawings may change in the near future, since modern CAD systems allow transfer to production not 2D drawings, but electronic models and product drawings.

Об учебно-методическом комплексе дисциплины «Инженерная и компьютерная графика» в условиях модернизации курса начертательной геометрии

In connection with the use of machine-building enterprises to create new products of computer-aided design, which solve the problem in three-dimensional space, the problem of modernization of the course of descriptive geometry becomes relevant. The article describes the experience of the Department of descriptive geometry and drawing of the Ufa state aviation technical University for the modernization of the course of descriptive geometry. The questions of development of educational and methodical complex of the modernized discipline “engineering and computer graphics”, about its components which are prepared by Department and are used in educational process at training of bachelors in the directions which are included in the enlarged group of 150000 «Mechanical engineering» are in detail considered.

Компьютерная методика изучения начертательной геометрии. Техническое задание

Descriptive geometry, whose subject of study is three-dimensional real and imaginary objects, is available for a specific method both of knowledge deepening and gained knowledge control. Thus apart from visualization of graphic constructions is available a strictly logical sequence of their execution. Using a graphical editor instead of a ruler and compass not only and not so much facilitates routine operations for construction of circles, parallel and perpendicular lines, but allows literally touch geometric images. Choice of one of three methods such as construction, transformation or intermediaries ones, allows a student under testing not only to respond a specific question, but also to choose a more suitable way to solve this problem. Has been presented the description of computer program that allows quickly solve course problems with the prompt, if necessary. Other modes make it possible to exercise self-control or final control of gained knowledge. The program interface is multi-window structure enabling in sequence, on proposed 4–7 steps, solve a problem in the animation mode. A program feature is the absence of false (harmful for the study) questions as options. The right questions of another stage are used as alternative. When the answer to the question is wrong, than the principle of return is used. Have been offered stages and questions for solution of one of typical problems with illustration of a possible computer algorithm. Has been presented a help page variant. A set of tasks, covering the entire course of descriptive geometry, has been presented for a discussion. It has been noted that the described program’s pilot variant was developed and successfully implemented in educational process with use of all formulated principles and modes, including animation and the choice of points coordinates by the random number method.

Role of Descriptive geometry course in development of students’ spatial visualization skills

Spatial ability is of great importance for successful work in various fields such as computer graphics, engineering, architecture and cartography. A number of studies have demonstrated that Descriptive geometry courses have the potential to develop spatial skills. The aim of this study is to investigate the effect of Descriptive geometry course with the current method of teaching on the spatial skills of students at the Faculty of Civil Engineering at the Technical University of Kosice. The study was conducted by a pretest and posttest method. The first grade students studying in the winter term of 2016 to 2017 educational year served as a sample for the study. A significant difference between the pretest and posttest scores was revealed by using the Wilcoxon signed rank test. The findings showed that Descriptive geometry course has a positive impact on development of students’ spatial skills. Although, the Descriptive geometry course provides numerous benefits, it is often regarded by students as one of the most difficult courses. The use of dynamic geometry software with the ability to represent three-dimensional space allows students to overcome the difficulties associated with the plot of this course. The future plans within Descriptive geometry teaching include integration of the dynamic geometry software GeoGebra into the educational process which should lead to the innovation and facilitation of the Descriptive geometry course. Keywords: Spatial ability, mathematics education, engineering education

POINTS ON THE SPHERE SURFACE

Purpose. The extensive use of the computer-aided design system (CAD) in education and industry puts forward new demands on the scope, content and quality of up-to-date descriptive geometry course. The purpose of the work is topicality analysis of traditional descriptive geometry methods for 3D modelling and development of methodological recommendations for its teaching as a subject together with a selected CAD. Methodology. Conclusions about effectiveness and expedience of application of descriptive geometry methods are drawn on the basis of tools analysis and comparison of modern CADs and descriptive geometry for solving problems arising during 3D modelling. Generalization of teaching experience made it possible to give recommendations about optimization of the descriptive geometry course taking into account present-day requirements to professional skills of an engineer. Findings. CADs tools and descriptive geometry methods are compared by way of specific example to give the answer what is more suitable for solving problems arising during 3D modelling. Originality. We presented the methodological recommendations about optimization of descriptive geometry teaching together with a selected CAD. We proposed the conception of a modern textbook on descriptive geometry. First of all, the textbook must describe algorithms for solving problems by means of standard CAD tools exactly in 3D, not on the plane. It is desirable to accompany these algorithms by pictorial images in order to have an opportunity to grasp an idea quickly and implement it through methods of direct modeling in CAD application. We also touched practical problems of students’ motivation to ensure high effectiveness of graphical education. Practical value. This paper may be useful mainly for educators in the field of engineering graphics because it raises a vital question ‘Descriptive Geometry versus CAD’ which now has no definite answer. Topicality and teaching approaches of different solution methods of spatial problems by means of projections is subject of a dispute, taking into account that CAD tools are continuously updated. This paper by way of specific example shows some advantages and limitations of descriptive geometry and CAD, as well as touches the issues of their efficient joint application for teaching.